Sample size for linear mixed models

Compute an approximated sample size for linear mixed models (two-level-designs), based on power-calculation for standard design and adjusted for design effect for 2-level-designs.

samplesize_mixed(
  eff.size,
  df.n = NULL,
  power = 0.8,
  sig.level = 0.05,
  k,
  n,
  icc = 0.05
)

smpsize_lmm(
  eff.size,
  df.n = NULL,
  power = 0.8,
  sig.level = 0.05,
  k,
  n,
  icc = 0.05
)

Arguments

eff.size

Effect size.

df.n

Optional argument for the degrees of freedom for numerator. See 'Details'.

power

Power of test (1 minus Type II error probability).

sig.level

Significance level (Type I error probability).

k

Number of cluster groups (level-2-unit) in multilevel-design.

n

Optional, number of observations per cluster groups (level-2-unit) in multilevel-design.

icc

Expected intraclass correlation coefficient for multilevel-model.

Value

A list with two values: The number of subjects per cluster, and the total sample size for the linear mixed model.

Details

The sample size calculation is based on a power-calculation for the standard design. If df.n is not specified, a power-calculation for an unpaired two-sample t-test will be computed (using pwr.t.test of the pwr-package). If df.n is given, a power-calculation for general linear models will be computed (using pwr.f2.test of the pwr-package). The sample size of the standard design is then adjusted for the design effect of two-level-designs (see design_effect). Thus, the sample size calculation is appropriate in particular for two-level-designs (see Snijders 2005). Models that additionally include repeated measures (three-level-designs) may work as well, however, the computed sample size may be less accurate.

References

Cohen J. 1988. Statistical power analysis for the behavioral sciences (2nd ed.). Hillsdale,NJ: Lawrence Erlbaum.

Hsieh FY, Lavori PW, Cohen HJ, Feussner JR. 2003. An Overview of Variance Inflation Factors for Sample-Size Calculation. Evaluation and the Health Professions 26: 239-257.

Snijders TAB. 2005. Power and Sample Size in Multilevel Linear Models. In: Everitt BS, Howell DC (Hrsg.). Encyclopedia of Statistics in Behavioral Science. Chichester, UK: John Wiley and Sons, Ltd.

Examples

# Sample size for multilevel model with 30 cluster groups and a small to
# medium effect size (Cohen's d) of 0.3. 27 subjects per cluster and
# hence a total sample size of about 802 observations is needed.
samplesize_mixed(eff.size = .3, k = 30)
#> $`Subjects per Cluster`
#> [1] 27
#> 
#> $`Total Sample Size`
#> [1] 802
#> 

# Sample size for multilevel model with 20 cluster groups and a medium
# to large effect size for linear models of 0.2. Five subjects per cluster and
# hence a total sample size of about 107 observations is needed.
samplesize_mixed(eff.size = .2, df.n = 5, k = 20, power = .9)
#> $`Subjects per Cluster`
#> [1] 5
#> 
#> $`Total Sample Size`
#> [1] 107
#>